Phase and amplitude modes in a superconductor with interlayer pair tunneling

Chakravarty, Sudbø, Anderson, and Strong have introduced a simple model for high Tc oxides based on the effect of Cooper pair tunneling in a bilayer (with strength TJ) with s-wave pairing (g) in the layers. We discuss the order parameter fluctuations of this model. Besides the usual Anderson-Bogoliubov phase and Littlewood-Varma amplitude modes, we find new out-of-phase phase and amplitude modes. Their energy and damping depend critically on whether TJ>g or TJ<g. Such fluctuations in the relative phase and amplitude of two coupled condensates were first discussed in a different system by Leggett in 1966.